Demand for large-screen phones is growing emphatically in the UK, new data shows, with phones bigger than 4.9in accounting for nearly one quarter of shipments in the first quarter of 2014.

Tracking company Context, which monitors shipments of phones to retail suppliers, resellers and corporate accounts in the UK, says that there has been a dramatic rise in the number and proportion of smartphones with screens measuring 4.9in or above, compared to the iPhone 4 and 4S, which measure 3.5in, and the iPhone 5, 5C and 5S, which measure 4in.

The data confirms a growing consumer interest in larger smartphones, and comes ahead of what is rumoured to be a new, larger iPhone in the autumn.

Shipments of screens over 4.9in grew from just 7% of the total in the first quarter of 2013 to 23% in the same period in 2014, according to Context's data.

Screens below 4.2in - taking in all the iPhones, and also some smaller Android phones - went from being 62% of shipments in the first quarter of 2013 to 48% in the first quarter of 2014.

Smaller screens - such as the iPhone - are still popular but demand for larger ones is growing, according to data from Context. Photograph: PR/Context

In absolute terms, shipments of iPhone-sized screens fell only slightly, from 1.37m to 1.3m. But those sized 4.9in and above grew rapidly, from 0.14m to 0.66m.

"Giant" phones - with screens larger than 5.9in, such as HTC's One Max - saw the most rapid growth. From fewer than 100 sales in the first quarter of 2013, their sales grew 100-fold, peaking over Christmas - though even then only consisted of 1% of the burgeoning market.

All that points to a trend which Apple cannot resist, suggests Jeremy Davies of Context.

"Apple are going to have to do a 4.7-inch phone," he says. "But this isn't cannibalisation of the existing market. The overall market seems to be growing."

Separate data provided to the Guardian by Chitika suggests that Samsung has begun to slightly erode Apple's position in smartphones - but that other vendors are seeing little change.

Web statistics collected from Chitika's advertising network comparing June 2014 with January 2014 shows that Apple's share fell slightly, from 49.7% of browsing to 48.9%, down 0.8 percentage points. Samsung's share rose from 21.4% to 22.8%.

The main loser was BlackBerry, which saw its share fall from 16.8% to 15.0%, and Nokia, which fell from 2.8% to 2.5%. HTC, which released its M8 One flagship in March, saw a small rise, from 3.0% to 3.1%.

The figures are normalised to 100%, so that falls do not necessarily mean a fall in ownership of phones, but a change in the mix of overall ownership. The UK smartphone market is still expanding, though more slowly than in previous years.

Apple is widely expected to launch larger-screened models of iPhone in the autumn, where it is expected to take advantage of the "adaptive display" function in its iOS 8 software to allow third-party apps to work on bigger screens without specific rewriting.